RD Sharma 2020 solution class 9 chapter 13 Quadrilaterals Exercise 13.1

Exercise 13.1

Page-13.4

Question 1:

Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angles.

Answer 1:

Let the measure of the fourth angles be x°. We know that the sum of the angles of a quadrilateral is 360°.

Therefore,

Hence the measure of the fourth angle is .

Question 2:

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angles of the quadrilateral.

Answer 2:

We have ,.

So, let ,

,

And

By angle sum property of a quadrilateral, we get:

Also,

And

Similarly,

Hence, the four angles are ,,and .

Question 3:

The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
 

Answer 3:

We have, .

So, let ,

,

and

By angle sum property of a quadrilateral, we get:

Also,

And

Similarly,

Hence, the four angles are , , and  .

Question 4:

In a quadrilateal ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that ∠COD =$\frac{1}{2}$ (∠A + ∠B).

Answer 4:

The quadrilateral can be drawn as follows:

We have CO and DO as the bisectors of angles and respectively.

We need to prove that.

In ,We have,

…… (I)

By angle sum property of a quadrilateral, we have:

Putting in equation (I):

Hence proved.